M. I. Rabinovich | PubMed Health

PubMed1996

Overview: Synchronization and patterns in complex systems.

The theory of complex systems, such as neural assemblies or lattices of chaotic oscillators has generated many new problems including the synchronization or regularization of the cooperative behavior of systems consisting of chaotic elements, regular spatial patterns in "chaotic" lattices, and so on. A number of these problems were discussed at the International School in Nonlinear Science-95 (Nizhniy Novgorod, Russia). In this overview we try to formulate some of the most interesting problems that were discussed at that meeting. (c) 1996 American Institute of Physics.

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PubMed1994

Omega-dimension of chaotic time series.

New characteristics, Omega-dimension (D(Omega)) and spectral density of dimension (D'(Omega)), of deterministically generated irregular signals are proposed. They are the functions that are calculated employing spectral transformation such as filtering with limit transmission frequency Omega. The Omega-dimension of the time series generated by a dynamical system with a homogeneous strange attractor does not depend on Omega and coincides with the dimension measured using a standard technique. If the time series does not possess the similarity property as the time scale changes (i.e., it is multiscaled in time), the calculation of D(Omega) gives additional information on the properties of the signal. In particular, it allows for the estimation of additional degrees of freedom in the time series on signal transmission through the communication channel and preliminary processing.

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